A117444 Period 5: Repeat [0, 1, 2, -2, -1].

0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0

Offset

0,3

Comments

See the comments in A203571 concerning formulas of the n-th term of periodic sequences. - M. F. Hasler, Jan 13 2013

Links

Table of n, a(n) for n=0..75.

Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,-1).

Formula

G.f.: x*(1+3*x+x^2)/(1+x+x^2+x^3+x^4) = x*(1+2*x^2-2*x^3-x^4)/(1-x^5).

a(n) = (1/2)*Sum_{k=0..5} L(k*(k^2-n)/5), where L(j/p) is the Legendre symbol of j and p.

a(n) = sqrt(2+2/sqrt(5))*sin(2*Pi*n/5)-sqrt(2-2/sqrt(5))*sin(4*Pi*n/5).

a(n) = -2 + floor(23401/99999*10^(n+1)) mod 10. - Hieronymus Fischer, Jan 03 2013

a(n) = -2 + floor(863/1562*5^(n+1)) mod 5. - Hieronymus Fischer, Jan 04 2013

a(n) = 2 - ((2-n) mod 5). - Wesley Ivan Hurt, Jul 12 2014

a(n) = - a(n-1) - a(n-2) - a(n-3) - a(n-4). - Wesley Ivan Hurt, Sep 05 2022

Maple

A117444:=n->2 - ((2-n) mod 5): seq(A117444(n), n=0..50); # Wesley Ivan Hurt, Jul 12 2014

Mathematica

Table[2 - Mod[2 - n, 5], {n, 0, 50}] (* Wesley Ivan Hurt, Jul 12 2014 *)

Prog

(PARI) A117444(n)=4315*5^(n%5)\1562%5-2  \\ M. F. Hasler, Jan 13 2013
(PARI) A117444(n, p=[0, 1, 2, -2, -1])=p[n%#p+1] \\ M. F. Hasler, Jan 13 2013
(Magma) [2-((2-n) mod 5) : n in [0..50]]; // Wesley Ivan Hurt, Jul 12 2014

Crossrefs

Cf. A061347.

Sequence in context: A180424 A092339 A079693 * A257145 A253262 A015504

Adjacent sequences: A117441 A117442 A117443 * A117445 A117446 A117447

Keyword

easy,sign

Author

Paul Barry, Mar 16 2006

Extensions

More terms from Wesley Ivan Hurt, Jul 12 2014

Status

approved